{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "47ffbac2",
   "metadata": {
    "papermill": {
     "duration": 0.01696,
     "end_time": "2021-07-09T03:31:30.847478",
     "exception": false,
     "start_time": "2021-07-09T03:31:30.830518",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# `torchdyn`Quickstart\n",
    "\n",
    "`torchdyn` is a PyTorch library dedicated to neural differential equations and equilibrium models.\n",
    "\n",
    "Central to the `torchdyn` approach are continuous and implicit neural networks, where *depth* is taken to its infinite limit.\n",
    "\n",
    "This notebook serves as a gentle introduction to NeuralODE, concluding with a small overview of `torchdyn` features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f107f2dd",
   "metadata": {
    "papermill": {
     "duration": 0.949066,
     "end_time": "2021-07-09T03:31:31.806541",
     "exception": false,
     "start_time": "2021-07-09T03:31:30.857475",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from torchdyn.core import NeuralODE\n",
    "from torchdyn.datasets import *\n",
    "from torchdyn import *\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7c4d85be",
   "metadata": {
    "papermill": {
     "duration": 0.021497,
     "end_time": "2021-07-09T03:31:31.842451",
     "exception": false,
     "start_time": "2021-07-09T03:31:31.820954",
     "status": "completed"
    },
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "# quick run for automated notebook validation\n",
    "dry_run = False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8b06d1a",
   "metadata": {
    "papermill": {
     "duration": 0.010429,
     "end_time": "2021-07-09T03:31:31.901441",
     "exception": false,
     "start_time": "2021-07-09T03:31:31.891012",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Generate data from a static toy dataset \n",
    "\n",
    "We’ll be generating data from toy datasets. In torchdyn, we provide a wide range of datasets often use to benchmark and understand Neural ODEs. Here we will use the classic moons dataset and train a Neural ODE for binary classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6fc24851",
   "metadata": {
    "papermill": {
     "duration": 0.021708,
     "end_time": "2021-07-09T03:31:31.933509",
     "exception": false,
     "start_time": "2021-07-09T03:31:31.911801",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "d = ToyDataset()\n",
    "X, yn = d.generate(n_samples=512, noise=1e-1, dataset_type='moons')        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8d5d5faa",
   "metadata": {
    "papermill": {
     "duration": 3.099303,
     "end_time": "2021-07-09T03:31:35.047541",
     "exception": false,
     "start_time": "2021-07-09T03:31:31.948238",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "colors = ['orange', 'blue'] \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(len(X)):\n",
    "    ax.scatter(X[i,0], X[i,1], s=1, color=colors[yn[i].int()])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ff3f435",
   "metadata": {
    "papermill": {
     "duration": 0.010201,
     "end_time": "2021-07-09T03:31:35.070405",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.060204",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Generated data can be easily loaded in the dataloader with standard `PyTorch` calls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d425a65e",
   "metadata": {
    "papermill": {
     "duration": 0.030644,
     "end_time": "2021-07-09T03:31:35.111512",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.080868",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.utils.data as data\n",
    "device = torch.device(\"cpu\") # all of this works in GPU as well :)\n",
    "\n",
    "X_train = torch.Tensor(X).to(device)\n",
    "y_train = torch.LongTensor(yn.long()).to(device)\n",
    "train = data.TensorDataset(X_train, y_train)\n",
    "trainloader = data.DataLoader(train, batch_size=len(X), shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e726d21f",
   "metadata": {
    "papermill": {
     "duration": 0.010225,
     "end_time": "2021-07-09T03:31:35.137585",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.127360",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We utilize [Pytorch Lightning](https://github.com/PyTorchLightning/pytorch-lightning) to handle training loops, logging and general bookkeeping. This allows `torchdyn` and Neural Differential Equations to have access to modern best practices for training and experiment reproducibility. \n",
    "\n",
    "In particular, we combine modular `torchdyn` models with `LightningModules` via a `Learner` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4611c3a1",
   "metadata": {
    "papermill": {
     "duration": 0.031905,
     "end_time": "2021-07-09T03:31:35.179814",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.147909",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, t_span:torch.Tensor, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model, self.t_span = model, t_span\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        t_eval, y_hat = self.model(x, self.t_span)\n",
    "        y_hat = y_hat[-1] # select last point of solution trajectory\n",
    "        loss = nn.CrossEntropyLoss()(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2c3b359",
   "metadata": {
    "papermill": {
     "duration": 0.010158,
     "end_time": "2021-07-09T03:31:35.203791",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.193633",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Define a  Neural ODE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9de620dd",
   "metadata": {
    "papermill": {
     "duration": 0.010185,
     "end_time": "2021-07-09T03:31:35.224244",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.214059",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Analogously to most forward neural models we want to realize a map \n",
    "\n",
    "$$\n",
    "        x \\mapsto \\hat y\n",
    "$$\n",
    "\n",
    "where  $\\hat y$ becomes the best approximation of a true output $y$ given an input $x$.\n",
    "In torchdyn you can define very simple Neural ODE models of the form \n",
    "\n",
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(t) &= f(z(t), \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad t\\in[0,1]\n",
    "$$\n",
    "\n",
    "by just specifying a neural network $f$ and giving some simple settings.\n",
    "\n",
    "**Note:** This Neural ODE model is of *depth-invariant* type as neither $f$ explicitly depend on $s$ nor the parameters $\\theta$ are depth-varying. Together with their *depth-variant* counterpart with $s$ concatenated in the vector field was first proposed and implemented by [[Chen T. Q. et al, 2018]](https://arxiv.org/abs/1806.07366)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3807a4e5",
   "metadata": {
    "papermill": {
     "duration": 0.01017,
     "end_time": "2021-07-09T03:31:35.244710",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.234540",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Define the vector field (DEFunc) \n",
    "\n",
    "The first step is to define any PyTorch `torch.nn.Module`. This takes the role of the Neural ODE vector field $f(h,\\theta)$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "14134078",
   "metadata": {
    "papermill": {
     "duration": 0.026635,
     "end_time": "2021-07-09T03:31:35.281578",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.254943",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "f = nn.Sequential(\n",
    "        nn.Linear(2, 16),\n",
    "        nn.Tanh(),\n",
    "        nn.Linear(16, 2)                       \n",
    "    )\n",
    "t_span = torch.linspace(0, 1, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60e751bc",
   "metadata": {
    "papermill": {
     "duration": 0.010293,
     "end_time": "2021-07-09T03:31:35.306778",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.296485",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In this case we chose $f$ to be a simple MLP with one hidden layer and $\\tanh$ activation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b344be4e",
   "metadata": {
    "papermill": {
     "duration": 0.010434,
     "end_time": "2021-07-09T03:31:35.327650",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.317216",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Define the NeuralDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83a3c13",
   "metadata": {
    "papermill": {
     "duration": 0.010513,
     "end_time": "2021-07-09T03:31:35.348724",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.338211",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The final step to define a Neural ODE is to instantiate the torchdyn's class `NeuralDE` passing some customization arguments and `f` itself.\n",
    "\n",
    "In this case we specify:\n",
    "* we compute backward gradients with the `'adjoint'` method.\n",
    "* we will use the `'dopri5'` (Dormand-Prince) ODE solver from `torchdyn`, with no additional options;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b1e56617",
   "metadata": {
    "papermill": {
     "duration": 0.023707,
     "end_time": "2021-07-09T03:31:35.383043",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.359336",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your vector field callable (nn.Module) should have both time `t` and state `x` as arguments, we've wrapped it for you.\n"
     ]
    }
   ],
   "source": [
    "model = NeuralODE(f, sensitivity='adjoint', solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ea41473",
   "metadata": {
    "papermill": {
     "duration": 0.010626,
     "end_time": "2021-07-09T03:31:35.404283",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.393657",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Train the Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a186183",
   "metadata": {
    "papermill": {
     "duration": 0.010591,
     "end_time": "2021-07-09T03:31:35.425820",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.415229",
     "status": "completed"
    },
    "tags": [
     "dry-run"
    ]
   },
   "source": [
    "With the same forward method of `NeuralDE` objects you can quickly evaluate the entire trajectory of each data point in `X_train` on an interval `t_span`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ded3187e",
   "metadata": {
    "papermill": {
     "duration": 0.392432,
     "end_time": "2021-07-09T03:31:35.829101",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.436669",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "t_span = torch.linspace(0,1,100)\n",
    "t_eval, trajectory = model(X_train, t_span)\n",
    "trajectory = trajectory.detach().cpu()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e598baf",
   "metadata": {
    "papermill": {
     "duration": 0.010763,
     "end_time": "2021-07-09T03:31:35.851608",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.840845",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The numerical method used to solve a `NeuralODE` have great effect on its speed. Try retraining with the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bf0b1543",
   "metadata": {
    "papermill": {
     "duration": 0.698538,
     "end_time": "2021-07-09T03:31:36.561040",
     "exception": false,
     "start_time": "2021-07-09T03:31:35.862502",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type      | Params\n",
      "------------------------------------\n",
      "0 | model | NeuralODE | 82    \n",
      "------------------------------------\n",
      "82        Trainable params\n",
      "0         Non-trainable params\n",
      "82        Total params\n",
      "0.000     Total estimated model params size (MB)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your vector field callable (nn.Module) should have both time `t` and state `x` as arguments, we've wrapped it for you.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a5ff6c356cca436ebf8e07ebdeb70fac",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = nn.Sequential(\n",
    "        nn.Linear(2, 16),\n",
    "        nn.Tanh(),\n",
    "        nn.Linear(16, 2)                       \n",
    "    )\n",
    "\n",
    "model = NeuralODE(f, sensitivity='adjoint', solver='rk4', solver_adjoint='dopri5', atol_adjoint=1e-4, rtol_adjoint=1e-4).to(device)\n",
    "\n",
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=200, max_epochs=300)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a117e662",
   "metadata": {
    "papermill": {
     "duration": 0.011771,
     "end_time": "2021-07-09T03:31:36.585954",
     "exception": false,
     "start_time": "2021-07-09T03:31:36.574183",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Plot the Training Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f700fcfe",
   "metadata": {
    "papermill": {
     "duration": 0.011818,
     "end_time": "2021-07-09T03:31:36.609633",
     "exception": false,
     "start_time": "2021-07-09T03:31:36.597815",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can first plot the trajectories of the data points in the depth domain $s$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "04148d3a-2f1d-4fb3-9602-8263a08fec25",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_eval, trajectory = model(X_train, t_span)\n",
    "trajectory = trajectory.detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "55454689",
   "metadata": {
    "papermill": {
     "duration": 1.448812,
     "end_time": "2021-07-09T03:31:38.070488",
     "exception": false,
     "start_time": "2021-07-09T03:31:36.621676",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Dimension 1')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "color=['orange', 'blue']\n",
    "\n",
    "fig = plt.figure(figsize=(10,2))\n",
    "ax0 = fig.add_subplot(121)\n",
    "ax1 = fig.add_subplot(122)\n",
    "for i in range(500):\n",
    "    ax0.plot(t_span, trajectory[:,i,0], color=color[int(yn[i])], alpha=.1);\n",
    "    ax1.plot(t_span, trajectory[:,i,1], color=color[int(yn[i])], alpha=.1);\n",
    "ax0.set_xlabel(r\"$t$ [Depth]\") ; ax0.set_ylabel(r\"$h_0(t)$\")\n",
    "ax1.set_xlabel(r\"$t$ [Depth]\") ; ax1.set_ylabel(r\"$z_1(t)$\")\n",
    "ax0.set_title(\"Dimension 0\") ; ax1.set_title(\"Dimension 1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aa5ffac",
   "metadata": {
    "papermill": {
     "duration": 0.012306,
     "end_time": "2021-07-09T03:31:38.099980",
     "exception": false,
     "start_time": "2021-07-09T03:31:38.087674",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Then the trajectory in the *state-space*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b160381b",
   "metadata": {
    "papermill": {
     "duration": 0.04031,
     "end_time": "2021-07-09T03:31:38.152813",
     "exception": false,
     "start_time": "2021-07-09T03:31:38.112503",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "As you can see, the Neural ODE steers the data-points into regions of null loss with a continuous flow in the depth domain. Finally, we can also plot the learned vector field $f$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "896684ac",
   "metadata": {
    "papermill": {
     "duration": 0.68942,
     "end_time": "2021-07-09T03:31:38.855071",
     "exception": false,
     "start_time": "2021-07-09T03:31:38.165651",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x7f11ed2d5e50>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# evaluate vector field\n",
    "n_pts = 50\n",
    "x = torch.linspace(trajectory[:,:,0].min(), trajectory[:,:,0].max(), n_pts)\n",
    "y = torch.linspace(trajectory[:,:,1].min(), trajectory[:,:,1].max(), n_pts)\n",
    "X, Y = torch.meshgrid(x, y) ; z = torch.cat([X.reshape(-1,1), Y.reshape(-1,1)], 1)\n",
    "f = model.vf(0,z.to(device)).cpu().detach()\n",
    "fx, fy = f[:,0], f[:,1] ; fx, fy = fx.reshape(n_pts , n_pts), fy.reshape(n_pts, n_pts)\n",
    "# plot vector field and its intensity\n",
    "fig = plt.figure(figsize=(4, 4)) ; ax = fig.add_subplot(111)\n",
    "ax.streamplot(X.numpy().T, Y.numpy().T, fx.numpy().T, fy.numpy().T, color='black')\n",
    "ax.contourf(X.T, Y.T, torch.sqrt(fx.T**2+fy.T**2), cmap='RdYlBu')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1e50ea5",
   "metadata": {
    "papermill": {
     "duration": 0.013755,
     "end_time": "2021-07-09T03:31:38.886832",
     "exception": false,
     "start_time": "2021-07-09T03:31:38.873077",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Sweet! You trained your first Neural ODEs! Now you can proceed and learn about more advanced models with the next tutorials**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26b57fe0-a77a-4b71-ac6a-963b027b6608",
   "metadata": {},
   "source": [
    "## More about `torchdyn`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "dac37954-da39-45d4-950a-21e49858b270",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "from torchdyn.numerics import Euler, RungeKutta4, Tsitouras45, DormandPrince45, MSZero, Euler, HyperEuler\n",
    "from torchdyn.numerics import odeint, odeint_mshooting, Lorenz\n",
    "from torchdyn.core import ODEProblem, MultipleShootingProblem"
   ]
  },
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   "cell_type": "markdown",
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    "But wait! `torchdyn` has way more than `NeuralODEs`. If you wish to solve generic differential equations parallelizable both in space (initial conditions) as well in time, with parallel, but do not need neural networks inside the vector field, you can use our functional API like so:"
   ]
  },
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   "execution_count": 47,
   "id": "1b888ba6-c0cf-450f-995c-d74ebed81a05",
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   "source": [
    "x0 = torch.randn(8, 3) + 15\n",
    "t_span = torch.linspace(0, 3, 2000)\n",
    "sys = Lorenz()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "664fa60d-16b5-444b-9e2f-0f1323d8e8d4",
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    "t0 = time.time()\n",
    "t_eval, accurate_sol = odeint(sys, x0, t_span, solver='dopri5', atol=1e-6, rtol=1e-6)\n",
    "accurate_sol_time = time.time() - t0\n",
    "\n",
    "t0 = time.time()\n",
    "t_eval, base_sol = odeint(sys, x0, t_span, solver='euler')\n",
    "base_sol_time = time.time() - t0\n",
    "\n",
    "t0 = time.time()\n",
    "t_eval, rk4_sol = odeint(sys, x0, t_span, solver='rk4')\n",
    "rk4_sol_time = time.time() - t0\n",
    "\n",
    "t0 = time.time()\n",
    "t_eval, dp5_low_sol = odeint(sys, x0, t_span, solver='dopri5', atol=1e-3, rtol=1e-3)\n",
    "dp5_low_time = time.time() - t0\n",
    "\n",
    "t0 = time.time()\n",
    "t_eval, ms_sol = odeint_mshooting(sys, x0, t_span, solver='mszero', fine_steps=2, maxiter=4)\n",
    "ms_sol_time = time.time() - t0"
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   "cell_type": "markdown",
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   "source": [
    "Alternatively, you can wrap your vector field in a specific `*Problem` to perform sensitivity analysis and optimize for terminal as well as integral objectives:"
   ]
  },
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   "execution_count": 52,
   "id": "f8aee2cb-2a3b-4681-bc80-578a79155eee",
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   "source": [
    "prob = ODEProblem(sys, sensitivity='interpolated_adjoint', solver='dopri5', atol=1e-3, rtol=1e-3, \n",
    "                  solver_adjoint='tsit5', atol_adjoint=1e-3, rtol_adjoint=1e-3)\n",
    "t0 = time.time()\n",
    "t_eval, sol_torchdyn = prob.odeint(x0, t_span)\n",
    "t_end1 = time.time() - t0"
   ]
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   "id": "089902c8-8313-4021-990a-3cec048f9224",
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   "source": [
    "Our numerics suite includes other tools, such as a `odeint_hybrid` for hybrid systems (potentially stochastic and multi-mode). We have built our numerics suite from the ground up to be compatible with hybridized methods such as hypersolvers, where a base solver works in tandem with neural approximators to increase accuracy while retaining improved extrapolation capabilities. In fact, these methods can be called from the same API:"
   ]
  },
  {
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   "execution_count": 40,
   "id": "0889b770-f4b4-457d-8d86-a3fa03897f3d",
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   "source": [
    "class VanillaHyperNet(nn.Module):\n",
    "    def __init__(self, net):\n",
    "        super().__init__()\n",
    "        self.net = net\n",
    "        for p in self.net.parameters():\n",
    "            torch.nn.init.uniform_(p, 0, 1e-5)\n",
    "    def forward(self, t, x):\n",
    "        return self.net(x)"
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   "execution_count": 43,
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   "source": [
    "net = nn.Sequential(nn.Linear(3, 64), nn.Softplus(), nn.Linear(64, 64), nn.Softplus(), nn.Linear(64, 3))\n",
    "hypersolver = HyperEuler(VanillaHyperNet(net))\n",
    "t_eval, sol = odeint(sys, x0, t_span, solver=hypersolver) # note: this has to be trained!"
   ]
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    "We also provide an extensive set of tutorial subdivided into modules. Each tutorials deals with a specific aspect of continuous or implicit models, or showcases applications (control, generative modeling, forecasting, optimal control of ODEs and PDEs, graph node classification). Check `torchdyn/tutorials` for more information."
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